Propriétés qualitatives des solutions des équations de Hamilton-Jacobi [d'après A. Fathi, A. Siconolfi, P. Bernard]
Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque no. 317  (2008), Talk no. 975, p. 269-293
@incollection{AST_2008__317__269_0,
     author = {Roquejoffre, Jean-Michel},
     title = {Propri\'et\'es qualitatives des solutions des \'equations de Hamilton-Jacobi [d'apr\`es A. Fathi, A. Siconolfi, P. Bernard]},
     booktitle = {S\'eminaire Bourbaki - Volume 2006/2007  - Expos\'es 967-981},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {317},
     year = {2008},
     note = {talk:975},
     pages = {269-293},
     zbl = {1162.35003},
     mrnumber = {2487737},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2008__317__269_0}
}
Roquejoffre, Jean-Michel. Propriétés qualitatives des solutions des équations de Hamilton-Jacobi [d'après A. Fathi, A. Siconolfi, P. Bernard], in Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981, Astérisque, no. 317 (2008), Talk no. 975, pp. 269-293. http://www.numdam.org/item/AST_2008__317__269_0/

[1] G. Barles - Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques & Applications (Berlin), vol. 17, Springer, 1994. | MR 1613876 | Zbl 0819.35002

[2] G. Barles & B. Perthame - Discontinuons solutions of deterministic optimal stopping time problems, RAIRO Modél. Math. Anal. Numér. 21 (1987), p. 557-579. | Article | Numdam | MR 921827 | Zbl 0629.49017

[3] P. Bernard - Smooth critical sub-solutions of the HamiltonJacobi equation, à paraître dans Math. Research Letters. | MR 2318653 | Zbl 1125.37044

[4] P. Bernard, Existence of C 1,1 critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds, Ann. Scient. Éc. Norm. Sup. 40 (2007), p. 445-452. | Article | Numdam | MR 2493387 | Zbl 1133.35027

[5] P. Bernard & B. Buffoni - Optimal mass transportation and Mather theory, à paraître dans J. European Math. Society. | MR 2283105 | Zbl 1241.49025

[6] P. Bernard & B. Buffoni, The Monge problem for supercritical Mañé potentials on compact manifolds, Adv. Math. 207 (2006), p. 691-706. | Article | MR 2271983 | Zbl 1137.49037

[7] L. A. Caffarelli & X. Cabré - Fully nonlinear elliptic equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, 1995. | Article | MR 1351007 | Zbl 0834.35002

[8] P. Cannarsa & C. Sinestrari - Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications, 58, Birkhäuser, 2004. | MR 2041617 | Zbl 1095.49003

[9] M. G. Crandall, H. Ishii & P.-L. Lions - User's guide to viscosity solutions of second order partial differential équations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), p. 1-67. | Article | MR 1118699 | Zbl 0755.35015

[10] M. G. Crandall & P.-L. Lions - Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), p. 1-42. | Article | MR 690039 | Zbl 0599.35024

[11] A. Fathi - Solutions KAM faibles conjuguées et barrières de Peierls, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), p. 649-652. | Article | MR 1473840 | Zbl 0943.37031

[12] A. Fathi, Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), p. 1043-1046. | Article | MR 1451248 | Zbl 0885.58022

[13] A. Fathi, Orbites hétéroclines et ensemble de Peierls, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), p. 1213-1216. | Article | MR 1650195 | Zbl 0915.58033

[14] A. Fathi, Sur la convergence du semi-groupe de Lax-Oleinik, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), p. 267-270. | Article | MR 1650261 | Zbl 1052.37514

[15] A. Fathi, Weak KAM theory, Cambridge University Press, à paraître.

[16] A. Fathi & A. Siconolfi - Existence of C 1 critical subsolutions of the Hamilton-Jacobi equation, Invent. Math. 155 (2004), p. 363-388. | Article | MR 2031431 | Zbl 1061.58008

[17] H. Ishii - A simple, direct proof of uniqueness for solutions of the Hamilton- Jacobi equations of eikonal type, Proc. Amer. Math. Soc. 100 (1987), p. 247-251. | Article | MR 884461 | Zbl 0644.35017

[18] P.-L. Lions - Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, vol. 69, Pitman (Advanced Publishing Program), 1982. | MR 667669 | Zbl 0497.35001

[19] P.-L. Lions, G. Papanicolaou & S. Varadhan - Homogenization of Hamilton-Jacobi equations, prépublication.

[20] J. N. Mather - Variational construction of Connecting orbits, Ann. Inst. Fourier (Grenoble) 43 (1993), p. 1349-1386. | Article | Numdam | MR 1275203 | Zbl 0803.58019

[21] R. T. Rockafellar - Convex analysis, Princeton Landmarks in Mathematics, Princeton University Press, 1997, Reprint of the 1970 original, Princeton Paperbacks. | MR 1451876 | Zbl 0932.90001